Basic to modeling the influence of food quality in ecosystems is the notion that all organisms need multiple elements in their nutrition, and not always are those present in the right proportions. The element composition of an organism may differ substantially from the element composition of its food. Stoichiometry deals with this matter, however, the traditional use of stoichiometry in food webs is simplistic. Firstly, in traditional stoichiometry, multi-substrate transformations are modeled according to Liebig's law of the minimum, where a minimum-operator effectuates a switch between different metabolic modes, depending on which element limits biomass production. This switch makes the mathematical tractability of such models cumbersome. Secondly, classic stoichiometry generally bases itself on element limitation, whereas the elements considered are available in many forms. For instance, nitrogen may be present as a mineral, an amino-acid, or in refractory phenolic matrices. As amino-acids can be used at much higher efficiency than lignin from which amino acids can only be excised after high energy investments, the classic approach does not always do justice to the thermodynamics involved in biochemical transformations. As an alternative to the classic approach, this thesis explores the use of DEB, including synthesizing units (SUs) for the uptake and use of potentially limiting substrates. It is demonstrated that this approach is able to grasp macro-biochemical processes, such as growth and maintenance, on a physiologically sound basis.
The four chapters in this thesis treat a series of models with different levels of ecological detail concerning trophic transfer. These models all consist of a set of non-linear ordinary differential equations, and they are analyzed using bifurcation analysis, to study their long term behavior.
Chapter 1 considers a classic chemostat tri-trophic food chain model with a single explicitly modeled basal resource. As a deviation from the classic food chain, the top-predator is replaced with an omnivore, which predates on both a predator and a producer species. The focus of this chapter is on the effect of omnivory in the context of nutrient enrichment. While modest omnivory, figuring as a weak trophic link in the model, is expected to stabilize the food chain, nutrient enrichment is deemed to cause adverse effects. The model shows that omnivory may indeed stabilize nutrient enriched food chains. Low interaction strengths between the omnivore and the producer species promote this stabilizing effect. The model also predicts the existence of multiple stable states and thereby accentuates the potential for omnivory induced hysteresis loops.
Chapter 2 concentrates on the use of SUs in a physiologically based model of a copepod species. This chapter demonstrates that, unlike models in traditional stoichiometry, SUs are able to effectively capture multiple element limitation in zooplankton. The model developed here is a Dynamic Energy Budget model, in which copepods ingest algae of varying nutritional quality. The model divides assimilates among nitrogenous and non-nitrogenous reserve pools. Reserves are mobilized and used to meet costs for maintenance and reproduction of the copepod. This chapter points out the need to use physiologically based models to understand the effects of food quality.
Chapter 3 incorporates the model developed in chapter~2 into a DEB-based food web model of a simple basic structure. The web consists of a diatom population, feeding on mineral nitrogen and carbon and using light for photosynthesis, and grazed upon by copepods. Dead organic detritus is decomposed into minerals and excreted minerals are recycled. Both diatoms and copepods consist of three biomass components, namely structural biomass, nitrogenous reserves and a non-nitrogenous reserves. The mass-balance formulation requires keeping track of all carbon and nitrogen in the model, and this results in a relatively large number of model state variables for a bi-trophic food chain (ten in piece). The nutritional quality of diatoms to copepods depends on the mineral resource composition. The focus of the study is the effect of different mineral provisions on long-term dynamics of this food web. Similar to classic theory, the addition of mineral nitrogen can destabilize the food chain. In contrast, carbon depletion may have a similar effect, which shows that resource depletion may also destabilize food webs. The conclusion therefore holds that the nutritional balance may be important for the stability of food webs. In the model, carbon appears to be non-limiting to the diatom species, but although carbon enrichment is unable to stimulate growth of the diatom population, it does fuel the copepod population indirectly, through changes in diatom composition. Thus, the concept of nutrient limitation may apply well to any particular trophic group, it need not work at the ecosystem level.
In chapter 4, the step from small hypothetical food webs towards larger realistic ecosystems is made. The model studied in this chapter considers a top litter layer of a pine forest soil in Wekerom, The Netherlands. This ecosystem has been empirically studied in detail, so that its trophic structure is known well. The emphasis of this work is on the potential use of mechanistically based models in field ecology. The structure of the Wekerom system is as follows. Two routes of litter decomposition can be distinguished. Bacteria are generally responsible for the decomposition of labile litter fragments, while fungi break down stable litter components, such as lignin and hemi-cellulose. The model splits up litter into four components. These are nitrogenous and non-nitrogenous components, each of which both a stable and a labile organic form exists. In addition to the resources (i.e. the 4 litter types) and microbiota, the food web model describes the dynamics of fungivores and bacterivores, as well as soil omnivores, capable of breaking down litter and grazing on both bacteria and fungi. The associated model thus captures both elements of multiple resource availability and trophic structure. To maintain a manageable number of state variable and parameters, the model used is a Monod-type model. The focus is on the effect of changes in fresh litter composition on the dynamics of the food web. These changes relate directly to effects of eutrophication, elevated atmospheric CO2 and UV-B enhancement on the composition of litter. The ecosystem is in stable equilibrium in all of the scenario's tested. However, the persistence of higher trophic groups may be threatened by changes in environmental circumstances. The activity of lower trophic levels is hardly affected by litter composition. The modeling results should, however, been interpreted with caution. A number of model parameters have not been measured in field experiments. On the bright side is that the model therefore gives direction to experimental research finding proper parameter values. The conclusion of this study is that the use of mechanistic models is inevitable for the understanding of the long-term dynamics of natural ecosystems, but the knowledge upon which the models base is still limited. This points out that collaborations between theoreticians and experimentalists should be stimulated.
The work presented in this dissertation yields a number of general ideas on the dynamics of ecosystems, as dependent on food web structure and resource availability. Here, omnivory stands model for weak trophic interactions. This thesis firstly treats a traditional food chain model with omnivory, and then explores a series of models each diverting in a different direction from the traditional modeling philosophy. In the traditional food chain model, with low biological detail, omnivory may act as a stabilizing factor in the food chain. The next question is whether inclusion of biological detail alone may stabilize food chains. A methodology for including physiological detail in population models is brought forward. It appeared that the stability properties of the physiologically based food chain model are similar to those of traditional food chain models. The inclusion of physiological detail does not promote stability in the associated model. To the contrary, recycling, an important feature in natural systems, potentially destabilizes the food chain. The implementation of organismal physiology comes with an increased model complexity. On the other hand, it facilitates the quantitative use in ecosystem studies and makes the models more suitable for experimental backup. Adding physiological detail in larger food webs with a higher connectance reduces the potential for oscillatory behavior. It is, for the time being, impossible to attribute the ubiquity of stable steady states in this model to weak trophic links. However, the combined results presented in this thesis suggest that the reticulate trophic interactions imposed on this model are responsible for food web stability. This suggestion could serve as a working hypothesis for food web studies in the years to come. Again, the inclusion of physiological realism makes the model suitable for experimental backup. In addition, the model exposes gaps in ecological knowledge. The expectation spoken out here is that only the collaboration between experimental ecologists and theoreticians will result in fundamental advance in ecology. While experimentalists need a mechanistic framework to design the proper experiments, modelers need empirical data to validate their results.
However, the model revealed that imbalances in nutrient provision, rather than enrichment, may be the cause of destabilization. Furthermore, both additions of carbon and nitrogen stimulate copepod population growth, which points out the need to be careful in applying the limitation of a single nutrient to ecosystem dynamics.
The content of this thesis has so far been published in the following papers: